| Unit name | Mechanics 2 |
|---|---|
| Unit code | MATH21900 |
| Credit points | 20 |
| Level of study | I/5 |
| Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |
| Unit director | Dr. Muller |
| Open unit status | Not open |
| Pre-requisites |
MATH11200, MATH11002 and MATH11003 |
| Co-requisites |
None |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
In Newtonian mechanics, the trajectory of a particle is governed by the second- order differential equation F = ma. An equivalent formulation, due to Maupertuis, Euler and Lagrange, determines the particle's trajectory as that path which minimises (or, at least, renders stationary) a certain quantity called the action. The mathematics which links these two formulations (which at first seem so strikingly different) is the calculus of variations. The known fundamental laws of physics (e.g. Maxwell's equations for electricity and magnetism, the equations of special and general relativity, and the laws of quantum mechanics) can be formulated in terms of variational principles, and indeed find their simplest expression in this way. The principle of least action in classical mechanics is conceptually one of the simplest, and historically on eof the first such examples. The course covers the principle of least action, the calculus of variations, the derivation of Lagrangian mechanics, and the relation between symmetry and conservation laws. Hamiltonian mechanics is introduced with a treatment of Poisson brackets and liouville's theorem. Applications will include the theory of small oscillations and rigid- body dynamics.
